Non-adiabatic crossing of symmetry breaking phase transitions results in formation of a domain structure and topological defects. The average density of domains depends on the quench rate of the phase transition. Kibble-Zurek mechanism predicts the scaling of the number of domains with quench rate. Phase transitions are ubiquitous in Nature and formation of domains and defects occurs in many different systems. One example of such system is Coulomb crystals of trapped ions, where structural defects can form as a result of symmetry breaking structural transitions between different crystal configurations. In the thesis, we investigate the Kibble-Zurek mechanism using the linear to zigzag structural phase transition in trapped ion Coulomb crystals. First, we analyse the equilibrium properties of crystals in the vicinity of the critical point of the linear to zigzag transition. Next, we show how to derive Kibble-Zurek scaling laws by transforming the equations of motion into a universal form. This mathematical derivation of the scaling laws is generalized for finite and inhomogeneous systems. Two experiments measuring the defect scaling in small trapped ion crystals are described, whose results agree with molecular dynamics simulations. In order to understand and predict defect dynamics we develop the technique for calculating the effective potential in which the defects move. Using this technique we show that heavy molecular ions stabilize the structural defects in zigzag chains and suggest a way of controlling kink motion using the application of electric fields. Finally, conclusions are drawn and possibilities for future work are suggested.

Terahertz (THz) radiation (≈ 0.1-10x10^12 Hz) is non-ionizing and its photon energies correspond to the rotational and vibrational modes of many complex molecules. Hence many substances of interest for biological and security applications can be detected using THz light; making THz spectroscopy an ideal tool for bio- and security sensing. However, a size mismatch between the photon wavelength and the size of many commonly sensed targets, and a lack of powerful sources hamper the progress of THz technology towards more widespread real-world applications. The focus of this thesis is to use novel concepts in the field of metamaterials to overcome or side step some of these challenges. In particular, the use of confined electromagnetic surface modes, such as lattice resonances and spoof plasmons, on metamaterial surfaces to conduct THz sensing is investigated. Different ways in which sensing information can be extracted from these specially structured metamaterial surfaces are explored so as to demonstrate the feasibility and versatility of metamaterial surfaces in THz sensing applications. The application of lattice resonances to detect refractive index changes caused by various fluids on an array of metallic rods is first reported in this thesis. This can be seen as a prelude to the work presented in later chapters where strongly confined spoof plasmons are employed for THz sensing. A metamaterial surface supporting spoof plasmons (simply termed as a Spoof Plasmon Surface (SPS)), consisting of a linear array of metallised sub-wavelength grooves, is filled with various fluids and shown to be capable of high performance refractive index sensing in an Otto prism setup. Sharp phase changes, readily available from THz time-domain spectroscopy (THz-TDS), associated with the coupling of THz radiation to spoof plasmons are used as the readout response in this case to indicate changes in the refractive indices of the fluids filling the grooves. Building upon the initial work on spoof plasmon sensing, further investigations demonstrate the feasibility of SPSs as a versatile platform on which various forms of sensing information can be extracted by using THz radiation that is coupled in and out of spoof plasmons via the scattering edge coupling scheme. The time-domain signal from the SPS is analysed using a short- time Fourier transform (STFT), enabling the extraction of the broadband spoof plasmon dispersion with a single measurement as well as the attenuation coefficient with a minimum of two measurements. Broadband sensing is demonstrated, again by filling the grooves with various fluids, which results in changes in the spoof plasmon dispersion and attenuation coefficients. In addition, the observation of the absorption peak of α-lactose monohydrate at 1.37 THz due to the enhanced light- matter interactions on an SPS is demonstrated and opens the door towards a more spectroscopic approach to THz sensing using SPSs.

Two projects are presented in this thesis. The first project is an investigation into linewidth-narrowing phenomena of intersubband cavity polaritons (ICPs) in a microcavity/multi-quantum well sample through angle-resolved laser spectroscopy. Strong coupling of the vacuum field of the microcavity, and the intersubband transition (ISBT) of the multi-quantum well led to vacuum Rabi splitting of 12.4 meV of the ICP modes at room temperature in the absorbance spectra. The linewidths of the ICPs were found to be substantially narrowed (4.2 meV, at room temperature) at the anticrossing point, narrower than the bare ISBT and empty microcavity linewidths at room temperature (6.2 and 6 meV, respectively, at room temperature), and narrower than existing theory predicted. The same effect was observed at cryogenic temperatures. Narrowing was explained by the light effective mass of the ICP, rendering the ICP unaffected by interface roughness scattering of the multi-quantum well. The measurement of the narrow linewidths was made possible by the superior angular resolution of laser spectroscopy compared to previously-used thermal light sources. The second project consisted of the development of a Q switched Er 3+ ,Cr 3+ :YSGG laser, of 3 μm wavelength, with 76 mJ fundamental mode pulses in free-running mode. Q switching of the laser was investigated in order to produce short (<400 ns) laser pulses, using two 'slow' Q switch methods. The first, a rotating mirror Q switch, was found to produce pulses of ~10 mJ, with an optimum mirror rotation rate of 300 rotations per second. The second Q switch method, a 'polygon chopper Q switch' produced single pulses of energy ~4 mJ, using a rotating polygon as an optical chopper. From this Q switch, it was deduced that the longest Q switching time possible for Er 3+ ,Cr 3+ :YSGG, with any method of Q switching, was ~30 μs for single pulse operation, and ~80 μs for multiple pulses.

This thesis attempts to investigate the phenomenon of supersolidity, where a system exhibits both spontaneously broken translational and U(1) symmetries, in two different two dimensional systems, one fermionic and one bosonic. The fermionic system consists of two parallel GaAs quantum wells that are independently gated. This allows the electron and hole populations of the two layers to be independently varied. Using mean field theory, it will be shown that the zero temperature phase diagram of this system contains a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, analogous to that predicted to occur in superconductors. This phase has spontaneously broken U(1) and translational symmetries, and can therefore be thought of as a supersolid. This mean field analysis will be complemented by a Ginzburg-Landau approach, which will be used to confirm the results and to calculate the lattice structure of the FFLO order parameter. The bosonic system consists of a thin helium-4 film deposited on graphite. Recent experiments on this system have produced results that suggest the presence of a supersolid phase over a range of helium filling fractions, as well as the lack of a Kosterlitz-Thouless phase transition at finite temperature. An attempt to explain these results is made by applying mean field and Bogoliubov theories to a toy model at zero temperature.

The thesis reports on the design and data from a new experimental platform, which uses the supersonic ablated plasma flow from an inverse wire array z pinch to create a highly diagnosed interaction geometry for studying magnetised reverse shocks. The flow (v~10^7cm/s, Ms~4-5) is generated with a frozen in magnetic field (B~1-2T, ReM~100) at a level sufficient to affect the structure of the shocks created by its collision with a stationary planar obstacle. In addition to the expected accumulation of stagnated plasma material in a thin, high density (strong shock) layer at the obstacle surface, a separate detached shock-like transition is also observed upstream of the obstacle, first observed at a distance ~c/wpi. Measurements of the reverse shock profile from Thomson scattering, interferometry, and local magnetic field probes, show that this 'sub-shock' feature displays unusually small discontinuities in the plasma properties (velocity, density, temperature) despite the high Mach numbers of the flow. Analysis shows that this feature, which is weakly collisional during its formation phase, appears to be a consequence of the pile-up of magnetic flux brought by the flow, which accumulates at the obstacle surface and acts on the magnetised electrons of the flow. An apparent discrepancy between the field strength measured at the sub-shock and the magnetic pressure required to support it against the ram pressure of the flow is addressed towards the end of the thesis. Preliminary results using a newly fielded Faraday rotation diagnostic to measure the field distribution within the reverse shock structure suggests that a pressure balance is achieved via the generation of current loops within the region, which locally enhance the field strength. Future work is set out for continued investigation, including improvements to the diagnostic, and a proposal to adapt the wire array setup to study magnetic reconnection in colliding plasma flows.

This thesis presents the work on a new beamline for ultra-fast spectroscopy experiments, along with the study of a new ultra-fast spectroscopy technique for studying attosecond electron dynamics: XUV initiated high harmonic generation (XiHHG) XiHHG is an extension of the high harmonic generation (HHG) technique for ultra-fast spectroscopy. XiHHG replaces the tunnel ionisation in HHG with single photon ionisation, and thus an XUV field is used to ionise the electron and a colinear IR field is used to recombine the electron. A goal of this is that energetically deep levels of atoms and molecules can be probed without the need for a very strong IR field. The specifications of the new beamline required that it be entirely housed in a vacuum of pressures on the order of 1x10 -6 mbar. As all of the optics and experimental controls were also in vacuum, electronic feed-throughs were implemented and sophisticated data acquistion software was developed. As the nature of the data collected for these experiments is large in volume, significant time was also spent creating an analysis script to handle the data automatically. This enabled the data to be transmitted amongst experimenters with ease and accuracy. Preliminary experimental results are shown from the beamline, with some possible theoretical explanations investigated. Further theoretical work is required in order to fully interpret the experimental results.

In order for photovoltaic energy conversion to compete with conventional energy sources and become a realistic alternative source of low-carbon renewable energy, significant cost-per-watt reduction is required. One obvious way to achieve this is to increase the conversion efficiency of solar cells, which is currently limited to around 30% even with modern technology. The Intermediate Band Solar Cell (IBSC), the focus of this project, is a concept that promises photovoltaic power conversion efficiencies of up to 63.2% through the introduction of an extra energy band in the bandgap of a semiconductor. However, many attempts to achieve IBSCs using quantum dots superlattice show poor conversion efficiency due to their small absorption cross-section and short-lived intermediate state. In this project, we attempt to overcome this issue by proposing an innovative Photon Ratchet (PR) quantum well cascade structure designed to improve the efficiency, through increasing the absorption cross-section and the lifetime of electrons in the intermediate state. The goal of this project is to prove the benefits of this concept, both theoretically and experimentally. In this thesis, theoretical and experimental work on quantum well solar cells is presented. The basic concept of solar cells, IBSC and PR-IBSC as well as their advantages and disadvantages are discussed in chapter 1, along with theory of quantum mechanics and optical transitions in quantum wells. Chapter 2 focuses on theoretical work, which includes limiting efficiency calculation and fundamental loss calculation in solar cells, in order to determine the fundamental benefit of the PR-IBSC when compared with conventional IBSCs. The result of this work was published in Applied Physics Letter in 2012 to propose the concept of the PR-IBSC for the first time. Experimental work on existing quantum well solar cells is presented in chapter 3, along with basic characterisation techniques. The InGaAs quantum well with GaAs barrier in a p-i-n diode is optically and electrically characterised and we describe how we have observed an increase in photocurrent due to sequential absorption of photons via the intermediate band (IB), which arises from the one-dimensional confinement in the quantum well, for the first time. This is an important result and has been published in the Journal of Photovoltaics in 2014. In order to study the interband and inter-subband transitions in quantum wells individually, we also designed a new set of samples, along with their reference samples, which consist of n-i-n and p-i-n diodes with identical single quantum wells in the i-region. The details of the samples, along with a model which simulates the transitions in quantum wells and achieves basic characterisation of the samples, are presented in chapter 4. Finally, in chapter 5, we draw up our conclusions and future work on the new samples is discussed.

The aim of our experiment is to explore two methods of creating an ultracold dipolar gas which can subsequently be used to simulate quantum phenomena. The first method is to sympathetically cool polar molecules. In this case, the molecules are overlapped with ultracold lithium atoms, thus allowing the two clouds to thermalise through elastic collisions. The second method is to electrically polarise ultracold lithium atoms using an electric field of approximately 1MV/cm. This involves placing the atoms between two high voltage electrodes. This thesis describes and characterises the setup used to produce, trap and transport a cloud of lithium-7 atoms. The setup consists of a lithium oven, Zeeman slower, magneto-optical trap (MOT) and magnetic trap. Up to 2.3x10^8 atoms are loaded into the MOT with an initial temperature of 1.3 mK. By implementing a compressed MOT phase the temperature is reduced to 0.75 mK. Before transport, 23% of the MOT atoms are transferred into the magnetic trap, which has a lifetime of 1.53±0.01 s in the MOT chamber. Using a motorised translation stage to move the magnetic trapping coils, atomic transport over a distance of 44 cm from the MOT chamber to the science chamber has been demonstrated. The transport efficiency is 41%. In the science chamber the lifetime of the magnetic trap has been measured as 18.5±0.7 s. Experiments to optimise the absorption imaging system have also been carried out, highlighting the fact that a time and position dependent magnetic field is present after the trapping coils switch off. The feasibility of producing a 1MV/cm electric field has been investigated. By using indium tin oxide coated glass electrodes in an adjustable electrode mount, an electric field of approximately 0.2MV/cm has been generated. These electrodes were subsequently replaced with super-polished stainless steel electrodes which generated a field of 0.38MV/cm.

In a world where science is constantly challenged to solve problems of increasing complexity, light is paving new ways to gather information about the physical properties of matter. Among these properties, elasticity is becoming fundamental in the understanding and the diagnosis of several diseases. Current solutions to gather mechanical information, however, measure the response of a material to an applied excitation, which makes them invasive and limited by a low spatial resolution. In contrast with these techniques, Brillouin spectroscopy offers the unique solution to retrieve stiffness information from the spectrum of the light scattered by inherent thermal acoustic waves. The combination of Brillouin spectroscopy with confocal microscopy has yielded a confocal Brillouin microscope able to perform mechanical imaging in a non-invasive manner. This was used to investigate two different biological problems: on the one hand the stiffness variations in specific endothelium cells of the eye, aiming at a better understanding of the mechanisms responsible for glaucoma, and on the other the characterisation of the mechanical structures of blood vessels, which could provide fundamental information regarding the formation of atherosclerotic plaques. Following an investigation on the optimal geometry that minimises the spectral broadening caused by the collection of photons over a range of scattering angles, high resolution Brillouin imaging was obtained in a confocal backscattering arrangement. To the best of our knowledge this thesis presents, for the first time, sub-cellular Brillouin images. In particular, in vitro Brillouin images of single HUVEC cells were acquired to investigate the cell's mechanical response to the application of the Latrunculin-A drug. This analysis, together with the finding of a linear correlation between the Brillouin modulus and the standard Young's modulus, validates the technique as a feasible means of measuring stiffness. Following this assessment, Brillouin images of normal and diseased vessels were acquired showing that the atherosclerotic plaques had a lower stiffness compared to both diseased and healthy vessel walls. These results might encourage the application of confocal Brillouin microscopy as the tool of choice for the investigation of the arterial biomechanics.

The key research aim of the present thesis is the building of a universal set of quantum gates for a long wavelength trapped-ion quantum information processor. It is desired to realise quantum computation using microwave and radio wave sources in a linear ion trap, where a static magnetic field gradient has been added to enhance motional and atomic state coupling. Furthermore, the qubit is constructed with the intrinsic use of superposition states generated with the help of constant microwave fields in the background: dressed states. This technique is essential for the shielding of the quantum operations against the unavoidable effects of magnetic noise. After reviewing the preliminary results and discussing briefly an auxiliary experimental technique intrinsic to the set-up, we introduce the magnetic gradient coupling and the dressed state scheme. We then proceed to illustrate how single and multi-qubit gates can be realised within such a system. Theoretical arguments are supplemented by numerical simulation and sources of experimental noise are taken into account.